Recently, how to eliminate the influence of collective noise in quantum communication has become an urgent problem. To solve the problem of low qubit efficiency of the current quantum key agreement protocols under collective noise, we propose two improved quantum key agreement protocols immune to collective phase noise and collective rotation noise, respectively. These two protocols mainly make use of the correlation among logical quantum states, delay measurement technology, unitary operation, and multi-particle entangled states to ensure that the communication parties can fairly establish a shared key. The qubit efficiency of the protocols is up to 27.27%, which effectively improves the existing quantum key agreement protocols immune to collective noise.